The origin of the galaxy size-stellar metallicity relation: A semi-analytical perspective

TL;DR

This work addresses how stellar metallicity correlates with galaxy size and what physical processes drive this relation. By integrating direct MaNGA observations, a detailed semi-analytical model (L-GALAXIES), and an analytical gas-regulator framework, it demonstrates an anti-correlation between size and stellar metallicity at fixed stellar mass, strongest in more massive systems. The authors show that gravitational potential depth and star formation history are insufficient to explain the trend; instead, variations in star formation efficiency (SFE) and the metal content of inflows, coupled with gas recycling, naturally reproduce the observed relation. A key result is that SFE affects stellar metallicity primarily when galaxies are not in equilibrium, with the regime $T/\tau_{eq} \lesssim 20$ applicable to $M_{\rm star} \lesssim 10^{10.5} M_\odot$, while massive galaxies retain the relation through merger-driven evolution. The findings imply a link between galaxy structure, baryon cycling, and the galaxy–halo connection, offering testable predictions for halo mass offsets at fixed stellar mass and guiding future lensing and hydrodynamical studies.

Abstract

Stellar metallicity encodes the integrated effects of gas inflow, star formation, and feedback-driven outflow, yet its connection to galaxy structure remains poorly understood. Using SDSS-IV MaNGA, we present the direct observational evidence that, at fixed stellar mass, smaller central galaxies are systematically more metal-rich, with a Spearman's rank correlation coefficient reaching $R_{\rm s}\approx -0.4$. The semi-analytical model L-GALAXIES reproduces this anti-correlation, albeit with a stronger amplitude ($R_{\rm s}\approx -0.8$). Within this framework, the trend cannot be explained by differences in gravitational potential depth or star formation history. Instead, smaller galaxies attain higher stellar metallicities because their elevated star formation efficiencies accelerate chemical enrichment, and, at fixed stellar mass, they inhabit less massive haloes, which makes their recycled inflows more metal-rich. The gas-regulator model demonstrates that star formation efficiency affects stellar metallicity when the system has not long remained in equilibrium, which is shown to be the case for central galaxies with $M_{\rm star}\lesssim 10^{10.5}\rm M_\odot$ in both L-GALAXIES and observation. The model also suggests a testable signature that, at fixed stellar mass, larger or lower-metallicity galaxies should inhabit more massive haloes than their smaller and higher-metallicity counterparts, providing a direct and testable imprint of the galaxy size-stellar metallicity relation on the galaxy-halo connection.

Figures (12)

• Figure 1: Top panel: The stellar mass-stellar metallicity relation with color encoding the half-mass size for central galaxies in MaNGA pipe3d. Bottom panel: The stellar mess-size relation with color encoding the stellar metallicity for the same galaxy sample. At fixed stellar mass, smaller central galaxies have higher stellar metallicity than their extended counterparts. Similarly, higher-$Z_{\rm star}$ central galaxies are smaller than their lower-$Z_{\rm star}$ counterparts at fixed stellar mass.
• Figure 2: Top panel: Spearman's rank correlation coefficients between galaxy half-mass size and the stellar metallicity in 0.2-dex stellar mass bins for central galaxies in MaNGA pipe3d, with error bars show the standard deviation of 100 bootstrap sample. The solid line is a smoothing B-spline fit to the data points to show the trend. Bottom panels: The joint distribution of stellar metallicity and galaxy half-mass radius in selected stellar mass bins. The gray boxes shows the median stellar metallicity in bins of galaxy sizes, with the error bar shows 16-84th percentiles. The grey solid line shows the linear fitting to the median trend. In fixed stellar mass bins, stellar metallicity and galaxies are anti-correlated to each other, and the strength of this correlation increases from $\approx -0.2$ at $M_{\rm star}\sim 10^{9.5}\rm M_\odot$ to $\approx -0.4$ above $10^{10}\rm M_\odot$.
• Figure 3: Top panel: Spearman's correlation coefficients galaxy half-mass stellar size and stellar metallicity for central galaxies in L-GALAXIES calculated in 0.1-dex-width stellar mass bins. Bottom panels: The joint distribution of galaxy size and stellar metallicity in four selected stellar mass bins. The contour lines enclose 10, 40, and 70% of galaxies in each subsample. The grey boxes show the median stellar metallicity as a function of galaxy size, with error bars show the 16-84th percentiles. L-GALAXIES shows a strong anti-correlation between stellar metallicity and galaxy size, and the correlation strength is $\approx -0.8$ across the whole stellar mass range.
• Figure 4: Top panel: The symbols are Spearman's rank correlation coefficients between galaxy stellar size and galaxy stellar metallicity with in bins of stellar mass (0.1 dex) and $V_{\rm max}$ (0.1 dex). Bottom panel: The symbols are Spearman's rank correlation coefficients between galaxy stellar size and galaxy stellar metallicity with in bins of stellar mass (0.1 dex) and stellar age (0.1 dex). In both panels, the gray solid line shows the rank correlation coefficients with only stellar mass fixed. The anti-correlation between galaxy stellar size and galaxy stellar metallicity remains at the same level after fixing $V_{\rm max}$. This indicates that either gravitational potential or star formation history is responsible for the anti-correlation between galaxy stellar size and stellar metallicity.
• Figure 5: The surface SFE, $\Sigma_{\rm SFR}/\Sigma_{\rm gas}$ as a function of gas surface density $\Sigma_{\rm gas}$, for the L-GALAXIES implementation in ayromlouGalaxyFormationLGALAXIES2021. Results are shown for different gas metallicities ($Z_{\rm gas}$, left panel), galaxy sizes ($r_{\rm disc}$, middle panel), and maximum circular velocities of the host halo ($V_{\rm max}$, right panel). The surface SFE is regulated by these three factors, in a sense that higher $Z_{\rm gas}$, smaller $r_{\rm disc}$, and higher $V_{\rm max}$ lead to higher SFE.